The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment*

  • Authors:

  • Maria Mitradjieva;Per Olov Lindberg

  • Affiliations:

  • Institute of Technology, Linkö/ping University, SE-58183 Linkö/ping, Sweden;Department of Transport Science, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden/ and Department of Numerical Analysis, KTH

  • Venue:
  • Transportation Science
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, conjugate direction Frank-Wolfe CFW, bi-conjugate Frank-Wolfe BFW, and “partanized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to an origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements ensuring link flow stability. We also show that CFW is globally convergent. We further point at independent studies by other researchers that show that our methods compare favorably with recent bush-based and gradient projection algorithms on computers with several cores.